Finance in a Classical and Harrodian Cyclical Growth Model

This paper is an extension of an earlier working paper (“Finance and the Macroeconomic Process in a Classical Growth and Cycles Model,” Working Paper No. 253). The basic structure of the model remains unchanged in that it is based on a social accounting matrix (SAM) with endogenous money. Investment in circulating capital adds to output and investment in fixed capital adds to potential output. Driving the model’s fast adjustment process, which describes the disequilibrium adjustment between aggregate demand and supply, is the dual disequilibria relationship in which the excess of monetary injections over desired money holdings fuels spending in the markets for goods and services. This excess also spills over into the bond market and lowers the interest rate. The model’s slow adjustment process entails adjustments in fixed investment so that actual and normal (desired) capacity utilization fluctuate around each other. Over the long run investment is internally financed and regulated by the rate of profit. The current paper has three innovations. First, inventory investment is treated explicitly. Second, the SAM itself has been split into a current and capital account, thereby making it easier to derive the balance sheet counterpart of the flow matrix. Third, the paper discusses the stability properties of the 4 x 4 nonlinear differential equation system that describes the fast adjustment process. The key to stability is the negative feedback effect of business debt on investment. In the 4 x 4 case, a necessary condition for stability is that the reaction coefficient h2 on the debt term in the circulating investment equation be positive; a necessary and sufficient condition is that h2³h2* where h2* is some critical value. In crossing this critical value, the system undergoes a Hopf bifurcation. Finally, if the model is reduced to a 3 x 3 system by considering a budget deficit that is wholly bond financed, then necessary and sufficient conditions for stability can be derived using the “modified” Routh-Hurwitz conditions. These stability conditions, in this case, imply that h2 > 0.